At a briefing on the latest high school progress report grades this afternoon, Department of Education officials touted the small boost in the number of schools receiving the best grades, but warned that the high grades might not be fully warranted.

It wasn’t easy for schools to keep their graduation rates or progress grades up this year. For the first time, most students were required to pass five Regents exams before graduating, and schools’ college readiness rates were factored into their overall progress scores. Still, 72 percent of schools received As and Bs—up from 64.4 percent last year.

Chief Academic Officer Shael Polakow-Suransky told reporters that the gains showed that schools were able to meet the new challenges before them.

“When you set a high bar and you give people time as you phase it in, people rise to the challenge,” he said. ” I think it’s a real accomplishment … but we’re very interested in getting schools to push higher.”

But that could mean raising the threshold for a good progress report grade—necessary to stay off the city’s list of schools it might close—for the second time since the progress reports were designed in 2007.

“If everyone’s reached the goal that we’ve set, then we typically up it because we want to push people to keep striving higher,” Polakow-Suransky said. If that happens, he added, the department will announce the new cut-off point this winter, giving schools time to reset their expectations.

Regardless, Polakow-Suransky said the schools that received As and Bs all deserved them, given the “higher bar” set by the college readiness metrics, which make up 10 points out of 100 for each school. Last year, college readiness was measured, but not scored, and 24.7 percent of schools met the city’s standards. This year, that figure rose by one percentage point.

Officials singled out several schools with As for helping high-needs students meet the college readiness standard, including Bronx Latin and Excelsior Preparatory High School, small schools which opened just a few years into the Bloomberg administration.

Other schools that have struggled on recent progress report saw stronger-than-average college readiness scores, including John Dewey High School, which was almost closed earlier this year, and Herbert H. Lehman High School, which is on this year’s list of schools that might close even though it received six out of 10 points for college readiness and earned a B in that section.

Polakow-Suransky attributed the small overall college readiness gain to the emphasis on critical thinking skills found in the new Common Core curriculum standards, and a new program the city created for awarding credit to high school for special, advanced courses that once received no extra recognition.

“Most of the job of a high school is to meet the state standard for graduation, and we are slowly over the next few years changing the curriculum, changing the assessments, and changing the goals,” he said. “What we’re looking at really closely here is how do we motivate schools to introduce strong curriculum so that their kids actually have a shot at success when they leave.”